eig

Builtin index · Core maths

result = eig(A)

Input: A · Output: result

What it is

Eigenvalues (and, for symmetric A, real eigenvectors) of a square n×n Mat A.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = eig(A)`	`A` Matnot documented yet	`Model` —kind `"eig"` `values` Vec or CVeca length-`n` `Vec` if all eigenvalues are real, otherwise a length-`n` `CVec` `vectors` Matan `n×n` `Mat` of eigenvectors as columns when `A` is symmetric, otherwise `Nothing`	Returns a `Model` (kind `"eig"`) with fields `values` (a length-`n` `Vec` if all eigenvalues are real, otherwise a length-`n` `CVec`) and `vectors` (an `n×n` `Mat` of eigenvectors as columns when `A` is symmetric, otherwise `Nothing`).

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

sym = [2, 0; 0, 3]
e = eig(sym)
print("eigenvalues = {e.values}")
print("eigenvectors = {e.vectors}")

rot = [0, -1; 1, 0]     # a rotation-like matrix: eigenvalues +-i

er = eig(rot)
print("complex eigenvalues = {er.values}")
print("eigenvectors = {er.vectors}")   # none: rot isn't symmetric

output

eigenvalues = [2, 3]
eigenvectors = [1, 0; 0, 1]
complex eigenvalues = [1j, -1j]
eigenvectors = none

from numerics-dsp

How it works

eig(A) — eigenvalues (and, for a symmetric A, real eigenvectors — dispatched on symmetry, checked directly, not assumed). Model kind "eig", fields values (real if the input is symmetric, otherwise a CVec) and vectors (a Mat when symmetric, Nothing otherwise — a general matrix's eigenvectors would themselves be complex-valued, which isn't computed here, not silently approximated).

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.